Abstract
We investigate the distribution of large positive (and negative) values of the Euler–Kronecker constant γQ(D) of the quadratic field Q(D) as D varies over fundamental discriminants |D|≤x. We show that the distribution function of these values is very well approximated by that of an adequate probabilistic random model in a large uniform range. The main tools are an asymptotic formula for the Laplace transform of γQ(D) together with a careful saddle point analysis.
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